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Pairwise-comparison methods in multiple objective programming, with applications in a long-term energy-planning model. (English) Zbl 0578.90040

This paper is devoted to multi-objective linear programming. Let \(c^ i\), \(i=1,...,p\), be the objective vector, the proposed method classically relies on the minimization of a weighted Tchebycheff norm, namely \[ \min imize\quad \max_{i=1,...,p}w_ i[x^*_ i-(c^ i)^ Tx] \] where \(x^*\) is the ideal point in the objective space.
The original part of this paper concerns the determination of the weights \(w_ i\). The first step in this determination process consists of asking the decision maker (DM) which trade-off between two objectives he accepts for deviating from the ideal point. The DM’s qualitative answers are then translated into numerical ratios \(r_{ijk}\) (preference of objective i vs j for the DM k); afterwards these ratios are aggregated by means of a logarithmic regression. A significant and original effort is made to justify the above construction in the context of psychological literature about stimulus perception. Finally an application to long-term energy planning is presented. But as noticed by the authors this application is much more informative on the prejudices of the research members of the Dutch Ministry of Economic Affairs than on their understanding and confidence in the method.
Reviewer: J.-C.Pomerol

MSC:

90B50 Management decision making, including multiple objectives
90C31 Sensitivity, stability, parametric optimization
90C90 Applications of mathematical programming
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